Photon Number Resolving Superconducting Detector

ABSTRACT

A method of resolving a number of photons received by a photon detector includes optically coupling a waveguide to a superconducting wire having alternating narrow and wide portions; electrically coupling the superconducting wire to a current source; and electrically coupling an electrical contact in parallel with the superconducting wire. The electrical contact has a resistance less than a resistance of the superconducting wire while at least one narrow portion of the superconducting wire is in a non-superconducting state. The method includes providing to the superconducting wire, from the current source, a current configured to maintain the superconducting wire in a superconducting state in the absence of incident photons; receiving one or more photons via the waveguide; measuring an electrical property of the superconducting wire, proportional to a number of photons incident on the superconducting wire; and determining the number of received photons based on the electrical property.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/623,503, filed Dec. 17, 2019, which is a United States National StageApplication filed under 35 U.S.C. § 371 of PCT Patent Application SerialNo. PCT/US2019/030019 filed on Apr. 30, 2019, which claims the benefitof and priority to U.S. Patent Application No. 62/665,491 filed on May1, 2018, each of which is hereby incorporated by reference in itsentirety.

TECHNICAL FIELD

This relates generally to photon detectors, including but not limitedto, superconducting photon detectors.

BACKGROUND

Photon detectors are key components in many electronic devices.Ultra-sensitive photon detectors that are capable of detectingindividual photons (e.g., single photons) can be used in a variety ofapplications, such as optical communications, medical diagnostics, spaceresearch, and optical quantum information applications such as opticalquantum computing.

Because of many useful properties of superconductors, photon detectorsbased on superconductors are expected to have superior performance overconventional photon detectors.

SUMMARY

Some embodiments of the present invention provide a photon detector(e.g., capable of resolving a number of co-incident photons). The photondetector includes a superconducting wire having a plurality ofalternating narrow and wide portions, a current sourceelectrically-coupled to the superconducting wire and configured tosupply the superconducting wire with electrical current, and an opticalwaveguide optically coupled to the plurality of narrow portions of thesuperconducting wire.

Some embodiments of the present disclosure provide a method of resolvinga number of co-incident photons. The method includes optically couplinga waveguide to a superconducting wire having a plurality of alternatingnarrow and wide portions. The method further includes electricallycoupling the superconducting wire to a current source. The methodfurther includes providing a first current from the current source tothe superconducting wire. The first current is configured to maintainthe superconducting wire in a superconducting state in the absence ofincident photons. The method further includes receiving one or morephotons via the waveguide. The method further includes measuring anelectrical property of the superconducting wire, wherein the electricalproperty is proportional to a number of photons incident on thesuperconducting wire. The method further includes determining the numberof received photons based on the electrical property.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the various described implementations,reference should be made to the Detailed Description below, inconjunction with the following drawings in which like reference numeralsrefer to corresponding parts throughout the figures.

FIGS. 1A-1C show a superconducting photon detector circuit according tosome embodiments.

FIG. 2 shows a photon number resolving superconducting (PNRS) detectoraccording to some embodiments.

FIGS. 3A-3C illustrate the operation of a portion of the PNRS detectorunder the case of two incident photons according to some embodiments.

FIGS. 4A-4B show a PNRS detector integrated with an optical waveguideaccording to some embodiments.

FIGS. 5A-5C show an illustrative layout for a waveguide integrated PNRSdetector according to some embodiments.

FIG. 6 shows a waveguide integrated PRNS detector in accordance with oneor more embodiments.

FIG. 7 shows a probabilistic photon source coupled to a waveguideintegrated PRNS detector, in according to some embodiments.

FIG. 8 is a flow chart illustrating a method of resolving a number ofco-incident photons, in accordance with some embodiments.

Like reference numerals refer to corresponding parts throughout theseveral views of the drawings.

DETAILED DESCRIPTION

Reference will now be made in detail to implementations, examples ofwhich are illustrated in the accompanying drawings. In the followingdetailed description, numerous specific details are set forth in orderto provide a thorough understanding of the various describedimplementations. However, it will be apparent to one of ordinary skillin the art that the various described implementations may be practicedwithout these specific details. In other instances, well-known methods,procedures, components, circuits, and networks have not been describedin detail so as not to unnecessarily obscure aspects of theimplementations.

Many modifications and variations of this disclosure can be made withoutdeparting from its spirit and scope, as will be apparent to thoseskilled in the art. The specific implementations described herein areoffered by way of example only, and the disclosure is to be limited onlyby the terms of the appended claims, along with the full scope ofequivalents to which such claims are entitled.

As used herein, a “superconducting circuit” or “superconductor circuit”is a circuit having one or more superconducting materials. For example,a superconducting photodetector circuit is a photodetector circuit thatincludes one or more superconducting materials. As used herein, a“superconducting” material is a material that is capable of operating ina superconducting state (under particular conditions). For example, asuperconducting material is a material that operates as a superconductor(e.g., operates with zero or near zero electrical resistance) whencooled below a particular temperature (e.g., a critical temperature) andhaving less than a maximum current flowing through it. A superconductingmaterial is also called herein a superconduction-capable material. Thesuperconducting materials may also operate in an “off” state wherelittle or no current is present. In some implementations, thesuperconducting materials operate in a non-superconducting state duringwhich the materials have a non-zero electrical resistance (e.g., aresistance in the range of one thousand to ten thousand ohms). Forexample, in some cases, a superconducting material supplied with acurrent greater than a maximum superconducting current for thesuperconducting material transitions from a superconducting state withzero or near zero electrical resistance to a non-superconducting statewith non-zero electrical resistance. As an example, superconducting wire102, described below with respect to FIGS. 1A-1C, is a superconductingmaterial that is capable of operating in a superconducting state (e.g.,under particular operating conditions).

As used herein, a “wire” is a section of material configured fortransferring electrical current. In some implementations, a wireincludes a section of material conditionally capable of transferringelectrical current (e.g., a wire made of a superconducting material thatis capable of transferring electrical current while the wire ismaintained at a temperature below a critical temperature). Across-section of a wire (e.g., a cross-section that is perpendicular toa length of the wire) optionally has a geometric (e.g., flat or round)shape or a non-geometric shape. In some implementations, a length of awire is greater than a width or a thickness of the wire (e.g., thelength of a wire is at least 5, 6, 7, 8, 9, or 10 times greater than thewidth and the thickness of the wire). As used herein, a nanowire is awire having a width less than one micron and/or a thickness less thanone micron and need not be symmetric in cross section, e.g., can have athickness that is several times larger than its width and vice versa. Insome implementations, a nanowire has a width less than 100 nm and/or athickness less than 100 nm.

FIG. 1A shows the superconducting photon detector circuit 100 having acurrent source 104, a superconducting wire 102, and activation circuitry108. In some implementations, the circuit 100 is electrically-coupled toelectrical grounds 106. FIG. 1A also shows a readout circuit 112connected to the superconducting wire 102 (optionally via resistor(s)110). In some implementations, the ground 106-1 is electrically-coupled(e.g., electrically connected) with the ground 106-2. In someimplementations, the current source 104 is configured to supply anelectrical current to superconducting wire 102 that is below a maximumsuperconducting current for the superconducting wire 102 (e.g., 70%,80%, or 90% of the maximum superconducting current for thesuperconducting wire 102). In some implementations, the superconductingwire 102 is composed of a superconducting alloy such as a niobium alloy(e.g., niobium-germanium), molybdenum alloy, vanadium alloy or any othersuperconducting material. In some implementations, the size and shape ofwire 102 is configured to maximize sensitivity to single photons (e.g.,near-infrared single photons). For example, in some implementations, thewire 102 has a width less than 100 nm. In some implementations, the wire102 has a thickness less than 50 nm, or even less than 10 nm. While theexamples disclosed herein employ superconducting material for thedetector wire, in some embodiments, any material can be used (includinga non-superconducting material) as long as the material possesses asufficient photon-induced change in electrical conductivity.

In some implementations, the resistor(s) 110 can have a resistance thatis less than a resistance of the superconducting wire 102 while thesuperconducting wire 102 is in a non-superconducting state. In someimplementations, the resistor(s) 110 include one or more distinctcomponents. In some implementations, the resistor(s) 110 includes one ormore resistances inherent in readout circuit 112 and/or the connectionbetween readout circuit 112 and the superconducting wire 102.

In some implementations, the activation circuitry 108 is configured tocontrol the flow of current to the superconducting wire 102. In someimplementations, the activation circuitry 108 is configured to enableflow of current from the current source 104 to the superconducting wire102 only during predetermined time periods. In some implementations, theactivation circuitry 108 is configured to enable flow of current fromthe current source 104 to the superconducting wire 102 in response to anenable signal. In some implementations, the activation circuitry 108 isconfigured to enable flow of current from the current source 104 to thesuperconducting wire 102 in response to photon(s) incident on one ormore components of the activation circuitry 108. In someimplementations, the superconducting photodetector circuit 100 does notinclude the activation circuitry 108 and the current source 104 iscoupled directly to the superconducting wire 102.

FIGS. 1A-1C show a series of diagrams to further illustrate how asuperconducting wire, also referred to herein as a superconductingnanowire, can be employed as a photon detector in accordance with one ormore embodiments. As shown in FIG. 1A, at a first time, a current source104 can supply a current 114 that flows through superconducting wire102. In some implementations and instances, all of the current 114, orsubstantially all of the current 114 (e.g., 95%, 98%, or 99%), flowsthrough the superconducting wire 102 due to the wire 102 being in asuperconducting state having zero (or near zero) electrical resistance(and thus, a resistance lower than the resistance of resistor(s) 110).In some implementations and instances, the superconducting wire 102 canbe maintained at a temperature below a critical superconductingtemperature (e.g., 5 Kelvin) and the current 114 can be set to be belowa maximum superconducting current threshold for the superconducting wire102. Under these conditions, the superconducting wire 102 can operate ina superconducting state (denoted by the hash marks on the wire 102 inFIG. 1A) with nearly all the current from the current source flowingthrough it (and no current flowing through the resistor(s) 110.

FIG. 1B shows the superconducting photon detector circuit 100 at asecond time, right before one or more photon(s) 116 impinge upon thesuperconducting wire. At the second time, one or more photon(s) 116 canbe incident on the superconducting wire 102. In some instances, when thephoton(s) 116 are absorbed by the wire 102, the photon energy istransferred to the superconducting material and can raise the localtemperature of that segment of superconducting wire above the criticalsuperconducting temperature. Accordingly, in response to the absorptionof the photon, the wire 102 can transition from the superconductingstate to a non-superconducting state that has a resistance that is largecompared to the resistor(s) 110.

FIG. 1C shows the superconducting photodetector circuit 100 at a thirdtime, soon after absorption of the photon(s) 116. At the third time, thesuperconducting wire 102 has transitioned to the non-superconductingstate (denoted by the crosshatching of the wire 102 in FIG. 1C) inresponse to the absorption of the photon(s) 116. The superconductingwire 102 now has a non-zero resistance (at least a portion of the wireis in a non-superconducting, e.g., normal state) and therefore current118 will be forced through the resistor(s) 110 to the readout circuit112. In some implementations and instances, all of the current from thecurrent source 104, or substantially all of the current (e.g., 95%, 98%,or 99%), flows through the resistor(s) 110 when the wire is in thenon-superconducting state. This flow of current is due to theresistor(s) 110 having a lower resistance than the wire 102 while thewire is in the non-superconducting state. In some implementations, thecurrent 118 can be measured by the readout circuit 112.

The current 118 being supplied to the readout circuit 112 can provide anindication to a user that photon(s) 116 were detected by thesuperconducting photodetector circuit 100. However, because of thesensitivity of the superconducting wire 102 to the absorption of asingle photon, absorption of a single photon can drive the wire to thenon-superconducting state and absorption of any additional photons willnot appreciably change the amount of current that flows through theresistor(s) 110. Thus, the device shown in FIGS. 1A-1C is not an idealdetector if resolving the number of incident photons is desired.

FIG. 2 shows a photon number resolving superconducting (PNRS) detector200 according to some embodiments. The PNRS detector 200 is similar inoperation to that described above in reference to FIGS. 1A-1C exceptthat in this case, a number of photosensitive superconducting segmentsare connected in an electrical series arrangement. More specifically, acurrent source 202 is electrically-coupled to a superconducting wire203, e.g., via metal layer 205, and provides a current to the wire, withthe current provided being below the critical current to maintainsuperconductivity in the superconducting wire 203 (e.g., the electricalcurrent supplied by the current source 202 is selected so as to maintainthe superconducting wire 203 in a superconducting (e.g., zeroresistance) state in the absence of incident photons, which are incidentfrom an optical waveguide, discussed below). The superconducting wire203 includes a plurality of alternating narrow and wide portions (e.g.,a plurality of narrow portions 250 and at least one wide portion 252, inalternating fashion). An optical waveguide, embodiments of which arediscussed in greater detail below, is coupled to the plurality of narrowportions 250 of the superconducting wire 203. In use, photons within thewaveguide impinge the narrow portions 250 of superconducting wire 203,resulting in photon detection.

In some embodiments, the narrow portions 250 have a first width (e.g.,less than 100 nm) and the wide portions 252 have a second width that isgreater than the first width (e.g., greater than 150 nm).

In this embodiment, to enable multi-photon detection and discrimination,an array of photon sensitive superconducting wire segments (e.g., thenarrow portions 250 of superconducting wire 203) are connected in seriesand are connected to one another by larger bend portions (e.g., one ormore of the wide portions 252 of superconducting wire 203 are bent, orare shaped so as to direct current flowing through such portions toundergo changes in current flow direction of 90 degrees or more), alsoformed from superconducting material. In some embodiments, the narrowportions 250 of the superconducting wire 203 are straight (e.g., toreduce current crowding effects within the narrow portion). Thisgeometry results in a meandering superconducting wire with improveddevice yield characteristics because any bends are made in various wideportions 252 along the length of the wire and each narrow photonsensitive region (the thin segments) is a short and straight segmentthat can absorb a single photon yet not cause the entire superconductingwire to transition to the normal state. In addition, in contrast toparallel arrangements of nanowires, absorption of a single photon in onesegment does not result in an avalanche effect by which current from thesegment that has transitioned to the normal state is diverted to theremaining parallel segments, causing the critical current to be exceededin these segments as well. The details of the operation of thisarrangement are further described below in reference to FIGS. 3A-3C.

Additionally, in this embodiment, the superconducting wire 203 can beformed having a meandering geometry, such that the narrow segments arearrayed along a longitudinal direction (z-direction) of the detector. Toprovide for addressability of each segment during detection, a metallayer 205 can be disposed along one edge of the meandering wire, asshown. The metal layer 205 forms an electrical contact electricallycoupled in parallel with the superconducting wire 203. For example, themetal layer 205 can at least partially overlap with the bottom (or top)portions of each U-shaped bend portion, as shown in FIG. 2. As describedin more detail below in reference to FIGS. 3A-3C, the metal layer 205can provide a parallel electrical resistance across the leg portions ofeach U-shaped segment, thereby providing a shunting path for current toflow if any of the narrow segments absorb a photon and transition to thenon-superconducting state (or alternatively, if a narrow portion becomesdamaged and/or permanently resistive for any reason). Thus, using thearchitecture shown in FIG. 2, the resistance of the parallel combinationof the metal layer 205 and the meandering superconducting wire 203varies based on how many narrow segments are in the non-superconductingstate (i.e., how many single photons have been absorbed). This effectiveparallel resistance can then be measured using readout circuit 207,e.g., by measuring a corresponding voltage drop across the length of themetal layer 205 (e.g., the readout circuit is configured to measure thevoltage across the electrical contact, which comprises metal layer 205and is coupled in parallel with the superconducting wire 203).

In some embodiments, the PNRS detector 200 can be an integrated devicewith one or more components being disposed on, or in, one or more layersof material, e.g., the device can be formed as a planar integratedcircuit. For example, the superconducting wire 203 can be formed from asuperconductor layer (e.g., a thin film or the like) that itself can bepatterned onto the surface of a substrate layer 201. As already notedabove, the superconductor layer can be formed from any superconductingmaterial that has been deposited onto the substrate layer 201 via anysuitable process, e.g., by physical vapor deposition, chemical vapordeposition, atomic layer deposition, and the like. After deposition, themeander geometry can be subsequently patterned via any suitablepatterning process, e.g., dry or wet etching, reactive ion etching, andthe like. Likewise, the substrate layer 201 can include any suitablesubstrate material, e.g., a silicon substrate, a silicon-based substrate(such as a silicon nitride (SiN) substrate) and the like. In someembodiments, the substrate does not include an oxide layer, so as toreduce or prevent oxidation of the superconducting material layer.

Returning to the example shown in FIG. 2, the meandering shape can beformed from an array of bent (e.g., U-shaped) superconducting structureshaving alternating orientations and that are each distributed along thelongitudinal direction (z-direction) of the PNRS detector 200. EachU-shaped portion of the PNRS detector 200 includes two leg portions thatare connected to a base portion. For example, in the embodiment shown inFIG. 2, leg portions 203 a and 203 b abut a base portion 203 c to forman inverted U-shape portion 204 (and any number of similar U-shapedportions can be distributed along the z-direction to provide forincreased dynamic range, or reliability, of the detector). Furthermore,each leg portion can include a relatively narrow, photon-sensitivecentral wire segment, each end of which abuts a wider end segment. Forexample, the leg portion 203 a of inverted U-shaped portion 204 includescentral narrow wire segment 204 a, whose upper end abuts wider legportion 203 d and whose lower end abuts wider leg portion 203 e.

In the illustrative example shown in FIG. 2, the relatively narrow andstraight photosensitive wire segments serve as a series array of singlephoton detectors that each operate in a manner that is similar to wire102, described above in reference to FIGS. 1A-1C. The narrow segmentsare electrically-coupled to each other via the larger bend segments ofthe superconducting wire, and these lager bend segments can serve asphoton-insensitive buffer regions of the superconducting wire. While thetransition in thickness between each narrow central segment and wide armof each bend segment is shown to be abrupt in FIG. 2, any gradual,tapered transition can be used without departing from the scope of thepresent disclosure. For example, in some embodiments, thesuperconducting wire is tapered between the narrow portions and the wideportions to reduce current crowding effects. In some embodiments, curvedtransitions can be employed for the upper/lower bends of the largerU-shape bend regions (e.g., bend region 211), thereby minimizing currentcrowding phenomena that can be present in superconducting wires havingsharp bends.

In addition, the relative sizes of the narrow central segments and thelarger buffer regions are chosen such that, at the design wavelength, asingle photon can provide enough energy to cause the narrow segment totransition to a non-superconducting state, thereby raising the seriesresistance of that segment of the superconducting wire. In contrast, anyphoton that impinges one of the larger buffer regions may not cause thatentire region to transition to the non-superconducting state, but ratherwill create merely a local hotspot. For example, the transverse width(i.e., transverse to the current flow direction) of the thin segmentscan be approximately, 100 nm or greater and the transverse width of thelarger buffer regions can be approximately 150 nm or less. Due to therelatively large area in the buffer region, e.g., buffer region 213,there is sufficient space for the superconducting current 209 to beredistributed around any local hotspots 210 caused by an errant photonabsorption. Thus, even if a photon is absorbed by the buffer regions,the superconducting current can still proceed generally unimpeded downthe remaining portion of the device. Furthermore, any local heatingpresent in the central narrow segment can be generally contained withinthat segment (or can intrude only minimally into the larger width bufferregions), leaving the other, downstream portions of the wire in thesuperconducting state.

In view of the above, the PNRS detector geometry shown in FIG. 2 canprovide for a spatially selective detector that will preferentiallydetect photons that impinge along the length of the device only (alongthe z-direction) and will be generally insensitive to photons that areincident on the superconducting wire, if incident in a region that isoutside of a relatively narrow region defined by the length of thephoto-sensitive narrow segments. In other words, the active region 215for photon detection for a device having this geometry can be anelongated rectangle, as shown. As described in more detail below, suchan arrangement can be advantageous for photon number resolving detectionin an integrated optical device such as a linear waveguide. Suchdetectors can be useful in a number of optical systems, including, e.g.,as detectors within heralded photon sources (e.g., as described withreference to FIG. 7) used in a linear optical quantum computer.

FIGS. 3A-3C illustrate the operation of a portion of the PNRS detector200 under the case of two incident photons. FIG. 3A shows the state ofthe detector just before a first photon 303 is absorbed by a firstnarrow segment 305. Before the photon 303 is absorbed, the entire lengthof the superconducting wire 307 is in the superconducting state, andtherefore the entire (or majority of) current I that is output from thecurrent source 309 passes through the superconducting wire 307 andcompletely bypasses the resistors R1 and R2. In FIG. 3A, the resistorsare shown schematically but in the actual device, these resistors wouldbe formed by a continuous metal layer, e.g., metal layer 205 shown inFIG. 2. As shown, the PRNS detector includes a readout circuit 311electrically coupled to the superconducting wire 307. The readoutcircuit 311 is configured to measure an electrical property of thesuperconducting wire (e.g., a voltage across the superconducting wire307 or an impedance of the superconducting wire 307). For example, inthe state shown in FIG. 3A the output voltage measured by the readoutcircuit 311 is low, e.g., close to 0 V.

The narrow portions of the superconducting wire 307 are configured totransition from a superconducting (zero resistance) state to anon-superconducting (non-zero resistance) state in response to anincident photon from an optical waveguide (e.g., optical waveguide 403,FIGS. 4A-4B). After the photon 303 is absorbed by the first narrowsegment 305, the narrow segment 305 transitions to a resistive normalstate (also referred to as a non-superconducting state), and thereforecan be represented as a resistor R3, as shown in FIG. 3B. When thisoccurs (e.g., while narrow portion 305 of the superconducting wire is ina non-superconducting state), the electrical contact has a resistance R1that is less than a resistance R3 of the superconducting wire 307.Because R3 is much greater than R1, the current I is now forced throughR1 and then back into the remaining U-shaped meandering portion 308 ofthe superconducting wire 307, which is still in a superconducting state.At this point, the voltage drop measured by the readout circuit 311 inthis state is I*R1. Shortly after the photon 303 is absorbed, or evensimultaneously with the absorption of photon 303, a second photon 312can be absorbed by a second narrow segment 313. As before, this secondnarrow segment 313 will transition to the non-superconducting stateforming resistor R4, as shown schematically in FIG. 3C. Now, current isforced to pass through both resistors R1 and R2 and thus, the voltagedrop measured by the readout circuit 311 in this state is I*(R1+R2).

In view of the above, the PNRS detector can discriminate between asingle photon absorption or multiple photon absorptions because thevoltage drop at the readout circuit 311 depends on whether one of thenarrow segments of a particular U-shape meander has absorbed a photon,transitioned to the normal state, and forced its respective currentthrough its associated shunt resistor. More generally, in a PNRS havingm U-shaped meander portions, and resistors R1=R2=R_(m)=R, if n photonsare absorbed by n different photon sensitive segments of the U-shapedmeanders, the current is re-routed into n resistors, resulting in anoutput voltage of ˜I*n*R, which is proportional to the number ofabsorbed photons. In some embodiments, the number of U-shaped meanders mcan be made large compared to the number of photons that are expected tobe detected to minimize the chance that any given multi-photon detectionwill exceed the dynamic range of the detector. In this manner, theelectrical property of the superconductor 307 measured by the readoutcircuit 311 (e.g., voltage across the superconductor 307) is indicativeof a number of photons incident to the superconducting wire 307.

Note that, in some embodiments, the wide portions are sized so as toremain in the superconducting state regardless of a state of the narrowportions. For example, meandering portion 308 remains in asuperconducting state regardless of the state of narrow portion 313.

FIG. 4A shows a PNRS detector 401, similar to those already describedabove, but here integrated with an optical waveguide 403. In thisexample, the PNRS detector 401 can be used to detect photons that aretravelling in the optical waveguide 403. In this example, the linearoptical waveguide 403 is disposed within a central region of thesuperconducting wire 405, directly underneath (or above) the array ofphoto-sensitive wire segments. In some embodiments, the input of thewaveguide can be coupled to a photon source (not shown). Photonsgenerated by the photon source are coupled into the waveguide andeventually arrive at the detector region shown in FIG. 4A. In someembodiments, the waveguide 403 and the meandering superconducting wire405 are positioned close enough to each other that it is possible for aphoton that is propagating in one of the guided modes of the waveguideto couple out of the waveguide and get absorbed by one of the narrowsegments after which it is detected by a readout circuit (not shown), asdescribed above. As shown in the cross section along A-A shown in FIG.4B (not to scale), in some embodiments, the optical waveguide 403 isvertically stacked with the superconducting layer 407 (e.g., withrespect to substrate 409). Superconducting layer 407 corresponds tosuperconducting wire 405 in FIG. 4B (e.g., superconducting wire 405 isformed from superconducting layer 407). The separation s between thewaveguide 403 and any given narrow segment of superconducting layer 407is approximately 100 nm or less. This allows for a weak, but non-zeroelectromagnetic coupling between the guided photons and thephoto-sensitive segments of superconducting wire. For example, in somecases the coupling could be on the order of 10% or less perphoto-sensitive segment (i.e., the probability of a photon absorption byany given segment is 10%). In such an arrangement, a superconductingwire having 10, 20, 30, 40, 50, or even more photo-sensitive segmentsmay be employed to increase the overall single/multi photon detectionefficiency. In addition, because the probability of detecting more thanone photon at the same photo-sensitive segment is relatively small, adevice such as this can also serve as a PNRS as described above (thephoton number is proportional to the number of individual narrowsegments that absorb a photon).

The waveguide integrated device shown in FIG. 4A can also be fabricatedas a planar integrated circuit, as shown in the cross-section of FIG.4B. In one embodiment, the base substrate 409 can be a flat siliconwafer. This silicon substrate can be covered by a high-quality siliconoxide layer 411. A waveguide 403 can be formed from silicon and disposedon the surface of the high-quality silicon oxide layer 411, and coveredby one or more capping layers, e.g., by a lower-quality silicon oxidelayer 413. The superconducting layer 407 that forms the superconductingnanowire is disposed on top of the lower-quality silicon oxide layer413. A metal layer 415 (e.g., an electrical contact) is disposed on theupper layer of the device, partially overlapping with both thelower-quality silicon oxide layer 413 and the superconducting layer 407.

While the waveguide 403 shown in FIG. 4A has a constant width w, othergeometries are possible without departing from the scope of the presentdisclosure. For example, to compensate for lower detection efficienciesof downstream narrow segments and thus to improve coupling, the opticalwaveguide is tapered in some embodiments, such that a downstream portionof the optical waveguide is wider than an upstream portion of theoptical waveguide. That is, as described in more detail below inreference to FIG. 6, the waveguide width can increase with increasinglength to improve the coupling efficiency of downstream photo-sensitivesegments relative to upstream photo-sensitive segments. Taperedwaveguide 403 a shows one such example (e.g., tapered waveguide 403 ahas width w that changes along the length of the tapered waveguide 403a, e.g., tapered waveguide 403 a has a narrow end 419 a and a wide end419 b, which is wider than the narrow end 419 a). In the PNRS shown inFIG. 4A, 8 photon-sensitive photo-sensitive segments are used asindividual photon detection regions but any number of photo-sensitivesegments can be used having any desired coupling efficiency to thewaveguide without departing from the scope of the present disclosure. Insome embodiments, PNRS detector 401 includes a mirror 417 disposed at anend of waveguide 403 (e.g., either a straight waveguide 403 or taperedwaveguide 403 a, although mirror 417 is shown disposed at an end oftapered waveguide 403 a). In some embodiments, mirror 417 is a Braggmirror. In some embodiments, mirror 417 is a retroreflective mirror. Insome embodiments, mirror 417 is a loop mirror. When PNRS detector 401includes mirror 417, PRNS detector is a “multi-pass” mirror, meaningphotons may travel along waveguide 403 more than once (e.g., travelthrough the waveguide in one direction, reflect off of mirror 417, andthen travel in the opposite direction).

FIGS. 5A-5C show an illustrative layout for a waveguide integrated PNRSdetector 500 according to some embodiments. FIG. 5A shows a zoomed-outview that shows a configuration of leads 503 and 505 that provide theelectrical connections to one or more readout circuits (not shown),e.g., a high impedance >1 kOhm CMOS readout circuit or the like. Otherlower impedance readouts are also possible without departing from thescope of the present disclosure. FIG. 5A also shows leads 507 that areconnected to meandering superconducting wire 509 that provide forconnections to a current source (not shown). In some embodiments thereadout circuit and the current source circuitry can be located on- oroff-chip. FIG. 5A also shows a possible positioning for metal layer 511that provides for the resistive bypass as described above in referenceto FIGS. 2-3. Advantageously the layout of the metal layer 511 isgenerally insensitive to the precise relative positioning (in thez-direction) between the metal layer 511 and the meanderingsuperconducting wire 509.

FIG. 5B shows a zoomed in view of region 513 showing additional detailsrelated to the shape of the meandering superconducting wire 509. Asdescribed in FIG. 2, the superconducting wire includes several U-shapedportions that are connected in series, via photo-sensitive segments,with each U-shaped portion of the PNRS detector 200 including twovertical leg portions that are connected to a horizontal base portion.FIG. 5B also shows that the bends of the base portions can have circularor smoothly (e.g., continuously but not necessarily circular) curvededges 515 to reduce current crowding on the inner edges of the bends.

FIG. 5C shows a further zoomed in view showing additional detail relatedto region 517 shown in FIG. 5B. In particular, FIG. 5C shows that foreach bend in the U-shaped portion of the superconducting wire, theinside radius of curvature R is approximately equal to the width d ofthe leg portions 519 and 521 (e.g., each wide portion includes a bend,and an inside bend radius of each wide portion is equal to a width ofthe wide portion). In addition, FIG. 5C shows that the transitionbetween the leg portions 519 and 521 and the photo-sensitive centralsegments 523 and 525 can be a gradual tapered transition between the twothicknesses of superconducting wire.

FIG. 6 shows a waveguide integrated PRNS detector 600 in accordance withone or more embodiments. In this example, a superconducting wire 603 isformed having multiple U-shaped bends as before, with a resistive metallayer 611 disposed on one edge, except that in this example, a bentwaveguide 605 is positioned adjacent to the superconducting wire 603(e.g., on the same layer of the chip but spaced horizontally apart fromthe superconducting wire). In this example, each U-shaped portion of thesuperconducting wire 603 includes an upper photo-sensitive segment,e.g., segment 607, that, like in the devices described above, cantransition to a non-superconducting state upon absorption of a photonthat is coupled out of the adjacent waveguide 605. Such a bent-waveguidearrangement can be advantageous because the separation d between thewaveguide and the photo-sensitive segment can be chosen precisely andindependently for each segment, something that is difficult to achieveif the waveguide and superconducting wire are manufactured on differentlayers of the chip.

In some embodiments, the optical waveguide 605 is positioned so that afirst coupling portion 652 a is separated from a first narrow portion650 a (e.g., segment) of the superconducting wire 603 by a firstdistance such that the first coupling portion is evanescently coupled tothe first narrow portion. A second coupling portion 652 b, downstreamfrom the first coupling portion, is separated from a second narrowportion 650 a of the superconducting wire 603 by a second distance, lessthan the first distance, such that a coupling efficiency between thesecond coupling portion and the second narrow portion is greater than acoupling efficiency between the first coupling portion and the firstnarrow portion. More specifically, the distance d between the waveguideand the photo-sensitive segment can be decreased as a function of thelongitudinal position along the waveguide (along the direction of photonpropagation 613). In general, the geometric coupling efficiency betweena waveguide and a superconducting wire segment increases with decreasingseparation d. Thus, in the device shown in FIG. 6, the geometriccoupling efficiency of the first segment 607 is smaller than thegeometric coupling efficiency of the last segment 609. Such a design canbe helpful to ensure a tighter distribution of overall detectorefficiencies in the presence of manufacturing defects relative to adesign that employs a flat waveguide with constant separation betweenthe superconducting segments along the length of the waveguide. The factthat such a design change can result in a tighter distribution ofdetector efficiencies for manufactured devices can be understood bynoting that in the straight waveguide (constant d) case, the probabilitythat the first segment will absorb a photon is higher than theprobability that the last segment will absorb a photon (the moresegments that are present in the photon's path before the last segment,the higher the probability that the photon will be absorbed before iteven reaches the last segment). Because of this effect, a defect orfailure in the first segment can have a much more dramatic effect onoverall detector efficiency than a defect or failure in the lastsegment, with this effect being accentuated for long detectors thatinclude many photo-sensitive segments. In the embodiment shown in FIG. 6the effect of decreasing photon absorption probability in the lateroccurring segments is countered by decreasing the spacing between thewaveguide and superconducting segments, thereby increasing the couplingefficiency for these later occurring segments relative to the earlieroccurring segments.

In some embodiments the device described above can be employed in anapplication that calls for single photon detection or multi-photondetection. In either case, the device has the added advantage of adetector architecture that has a high efficiency (the more numerous thenarrow photo-sensitive segments, the higher the single photon detectionprobability and the higher the dynamic range of the multi-photondetector). In addition, embodiments disclosed herein will result inincreased yield relative to architectures that employ tight bends due tothe fact that in the embodiments disclosed herein, the narrowphotosensitive segments are straight and relatively short compared tothe overall larger meander structures. Thus, because embodimentsdisclosed herein include fewer sharp bends in the narrow segments thedevices will be subject to fewer nanofabrication defects therebyincreasing device yield. Additionally, embodiments disclosed hereinprovide for increased operational reliability because even in the eventof a complete failure (open circuit) of one of the narrow segments, theparallel resistor formed from the metal layer will re-route themeasurement current around the failure and the device will continue tofunction, albeit at slightly reduced efficiency (this is to be comparedto a pure series arrangement, without the metal resistor layer, wherefailure of one segment results in a total failure of the detector).

FIG. 7 shows an optical device 700 that includes a photon source 702coupled to a waveguide integrated PRNS detector 600, according to someembodiments. In some embodiments, photon source 702 is a probabilisticphoton source. For example, photon source 702 has a photon-numberdistribution (e.g., a distribution of numbers of photons produced perattempt) with a non-zero variance. In some embodiments, photon source702 is most likely to, on a respective attempt, produce zero photons(e.g., there is a 90% probability of producing zero photons per attemptto produce a single-photon). The second most likely result for anattempt is production of a single-photon (e.g., there is a 9%probability of producing a single-photon per attempt to produce asingle-photon). The third most likely result for an attempt isproduction of two photons (e.g., there is a 1% probability of producingtwo photons per attempt to produce a single-photon). In somecircumstances, there is less than 1% probability of producing more thantwo photons.

In some embodiments, optical device 700 is configured to produceheralded single-photons. Heralded single-photons can be produced in avariety of ways. For example, in some embodiments, the photon sources702 include a laser or any other light source, e.g., LEDs, and the like.In embodiments in which photon source 702 is a laser, the laser producesa laser beam, referred to as a pump or a pump beam (which includes pumpphotons). In some embodiments, the laser produces many photons eithercontinuously or in bursts (e.g., pulses). A photon pair is created byconverting one pump photon into a pair of photons having lower energythan the pump photon (e.g., using a material having a second-ordernon-linear coefficient, which is optionally included in photon source702). One of the photons is passed to PRNS detector 600 via waveguide704 a (e.g., optically coupled to waveguide 605 of PRNS detector 600),which is then used to herald the presence of the other one of thephotons (e.g., in waveguide 704 b).

Alternatively, in some embodiments, two photons from a pump areconverted into a pair of photons. One photon of the pair of photons hasa lower energy than a respective pump photon. The other photon of thepair of photons has higher energy than the respective pump photon. Oneof the photons (e.g., either the higher-energy photon or thelower-energy photon) is then used to herald the presence of the otherphoton.

FIG. 8 is a flow chart illustrating a method of resolving a number ofco-incident photons, in accordance with some embodiments. In someembodiments, the method 800 is performed by any of the photon detectorsdescribed herein (e.g., a photon number resolving superconducting (PNRS)detector 200, FIG. 2, PNRS detector 401, FIG. 4, integrated PNRSdetector 500, FIG. 5, and/or PRNS detector 600, FIG. 6).

The method 800 includes optically coupling (802) a waveguide (e.g., anoptical waveguide) to a superconducting wire having a plurality ofalternating narrow and wide portions. In some embodiments, opticallycoupling the waveguide to a superconducting wire includes positioningthe waveguide so that a first coupling portion of the waveguide isseparated from a first narrow portion of the superconducting wire by afirst distance such that the first coupling portion is evanescentlycoupled to the first narrow portion. In some embodiments, the waveguideincludes a plurality of coupling portions, and optically coupling thewaveguide to a superconducting wire includes positioning a secondcoupling portion, downstream from the first coupling portion, such thatthe second coupling portion (comprising one of the plurality of couplingportions of the waveguide) is separated from a second narrow portion ofthe superconducting wire by a second distance, less than the firstdistance, such that a coupling efficiency between the second couplingportion and the second narrow portion is greater than a couplingefficiency between the first coupling portion and the first narrowportion.

The method 800 further includes electrically coupling (804) thesuperconducting wire to a current source. The method 800 furtherincludes providing (806) a first current from the current source to thesuperconducting wire. The first current is configured to maintain thesuperconducting wire in a superconducting state in the absence ofincident photons (e.g., the first current is has a current densitywithin the narrow portions that is less than, but close to, a thresholdcurrent density for superconductivity of the narrow portions).

The method 800 further includes receiving (808) one or more photons viathe waveguide. In some embodiments, as explained below, the one or morephotons are received from a probabilistic photon source.

The method 800 further includes measuring (810) an electrical propertyof the superconducting wire, wherein the electrical property is afunction of (e.g., proportional to, or alternatively a non-linearfunction of) the number of photons incident on the superconducting wire.In some embodiments, the electrical property is a voltage across thesuperconducting wire or an impedance of the superconducting wire. Insome embodiments, the electrical property is indicative of a number ofphotons incident to the superconducting wire.

The method 800 further includes determining (812) the number of receivedphotons based on the electrical property (e.g., by determining acorrespondence between the measured electrical property and the numberof received photons).

In some embodiments, the method 800 includes coupling a photon source(e.g., a probabilistic photon source) to the optical waveguide. In someembodiments, the method 800 includes attempting to generate a photonusing the photon source (e.g., gating the photon source). In someembodiments, the method 800 includes converting a photon produced by thephoton source into a pair of photons. In some embodiments, the method800 further includes detecting a respective photon of the pair ofphotons to herald the presence of the other photon of the pair ofphotons. In some embodiments, the method 800 includes outputting abinary value in accordance with a determination that a photon wasdetecting, the binary value indicating (e.g., heralding) the presence ofthe other photon.

Although some of various drawings illustrate a number of device stagesin a particular order, stages that are not order dependent may bereordered and other stages may be combined or broken out. While somereordering or other groupings are specifically mentioned, others will beobvious to those of ordinary skill in the art, so the ordering andgroupings presented herein are not an exhaustive list of alternatives.Moreover, it should be recognized that the stages could be implementedin hardware, firmware, software or any combination thereof.

It will also be understood that, although the terms first, second, etc.are, in some instances, used herein to describe various elements, theseelements should not be limited by these terms. These terms are only usedto distinguish one element from another. For example, a first protectivelayer could be termed a second protective layer, and, similarly, asecond protective layer could be termed a first protective layer,without departing from the scope of the various describedimplementations. The first protective layer and the second protectivelayer are both protective layers, but they are not the same protectivelayer unless explicitly stated as such.

The terminology used in the description of the various describedimplementations herein is for the purpose of describing particularimplementations only and is not intended to be limiting. As used in thedescription of the various described implementations and the appendedclaims, the singular forms “a”, “an” and “the” are intended to includethe plural forms as well, unless the context clearly indicatesotherwise. It will also be understood that the term “and/or” as usedherein refers to and encompasses any and all possible combinations ofone or more of the associated listed items. It will be furtherunderstood that the terms “includes,” “including,” “comprises,” and/or“comprising,” when used in this specification, specify the presence ofstated features, integers, steps, operations, elements, and/orcomponents, but do not preclude the presence or addition of one or moreother features, integers, steps, operations, elements, components,and/or groups thereof.

The foregoing description, for purpose of explanation, has beendescribed with reference to specific implementations. However, theillustrative discussions above are not intended to be exhaustive or tolimit the scope of the claims to the precise forms disclosed. Manymodifications and variations are possible in view of the aboveteachings. The implementations were chosen in order to best explain theprinciples underlying the claims and their practical applications, tothereby enable others skilled in the art to best use the implementationswith various modifications as are suited to the particular usescontemplated.

What is claimed is:
 1. A method of resolving a number of co-incidentphotons, comprising: optically coupling a waveguide to a superconductingwire having a plurality of alternating narrow and wide portions;electrically coupling the superconducting wire to a current source;electrically coupling an electrical contact in parallel with thesuperconducting wire, wherein the electrical contact has a resistancethat is less than a resistance of the superconducting wire while atleast one narrow portion of the superconducting wire is in anon-superconducting state; providing a first current from the currentsource to the superconducting wire, the first current configured tomaintain the superconducting wire in a superconducting state in theabsence of incident photons; receiving one or more photons via thewaveguide; measuring an electrical property of the superconducting wire,wherein the electrical property is proportional to a number of photonsincident on the superconducting wire; and determining the number ofreceived photons based on the electrical property.
 2. The method ofclaim 1, wherein each narrow portion of the plurality of narrow portionsis straight to reduce current crowding effects within the narrowportion.
 3. The method of claim 1, wherein at least one wide portion ofthe plurality of wide portions is bent.
 4. The method of claim 1,wherein the narrow portions each have a first width and the wideportions each have a second width, the second width being greater thanthe first width.
 5. The method of claim 1, wherein the narrow portionsof the superconducting wire are configured to transition from asuperconducting state to a non-superconducting state in response to anincident photon from the optical waveguide.
 6. The method of claim 5,wherein the wide portions are sized so as to remain in thesuperconducting state regardless of a state of the narrow portions. 7.The method of claim 1, further comprising electrically coupling areadout circuit to the superconducting wire, wherein the readout circuitis configured to measure the electrical property of the superconductingwire, indicative of the number of photons incident to thesuperconducting wire.
 8. The method of claim 7, wherein the electricalproperty comprises a voltage across the superconducting wire or animpedance of the superconducting wire.
 9. The method of claim 7, whereinthe readout circuit is configured to measure a voltage across a contactcoupled in parallel with the superconducting wire.
 10. The method ofclaim 1, including outputting a binary value in accordance with adetermination that at least one photon was received, the binary valueindicating detection of at least one photon.
 11. The method of claim 1,wherein the optical waveguide is tapered to improve coupling, such thata downstream portion of the optical waveguide is wider than an upstreamportion of the optical waveguide.
 12. The method of claim 1, wherein thesuperconducting wire is tapered between the narrow portions and the wideportions to reduce current crowding effects.
 13. The method of claim 1,including coupling a photon source to the optical waveguide.
 14. Themethod of claim 1, wherein each wide portion includes a bend, andwherein an inside bend radius of each wide portion is equal to a widthof the wide portion.
 15. The method of claim 1, wherein the opticalwaveguide includes a plurality of coupling portions; and the opticalwaveguide is positioned so that a first coupling portion is separatedfrom a first narrow portion of the superconducting wire by a firstdistance such that the first coupling portion is evanescently coupled tothe first narrow portion.
 16. The method of claim 15, wherein a secondcoupling portion of the plurality of coupling portions, downstream fromthe first coupling portion, is separated from a second narrow portion ofthe superconducting wire by a second distance, less than the firstdistance, such that a coupling efficiency between the second couplingportion and the second narrow portion is greater than a couplingefficiency between the first coupling portion and the first narrowportion.